In wireless communication systems, Uplink (UL) signals transmitted by User Nodes (UNds) and received by Access Nodes (ANs) having antenna arrays that are affected by the scattering environment and in particular by the reflections of physical obstacles, such as buildings, vehicles, as well as mounting device for the ANs. These propagation effects may include cross-polarization and mutual coupling well know in the art. Knowledge of the overall influence of these propagation effects or imperfections to the antenna arrays is not required for Multiple Input Multiple Output (MIMO) communication purposes or for positioning based on Time-of-Arrival (ToA). Examples of UNds are User Equipments in Long Term Evolution (LTE) terminology and examples of ANs are base stations and access points.
However, information about such imperfections is needed in order to achieve highly accurate positioning of UNds based on Angle-of-Arrival (AoA). This operation is called calibration of the antenna array or antenna calibration. If the calibration of the antenna arrays is not performed, the AoA estimates cannot be used for positioning. Calibration of the antenna array means acquiring the behaviour of the antenna array, and in particular how the antenna array reacts to radio signals from different directions/locations in an area of the wireless communication system. The calibration of the antenna array is in this respect a software procedure.
The following conventional solutions can be used for calibrating antenna arrays:                The calibration of the antenna array is performed in anechoic chambers;        The propagation channel is estimated along with the calibration of the antenna array, which is known as auto-calibration;        Dedicated measurement campaigns on the site where the antenna array is deployed; and        UL data transmissions using precoding and/or beamforming for antenna array calibration.        
The aforementioned conventional solutions however have quite a few limitations.
Calibrating the antenna array in an anechoic chamber does not acquire the influence of the mounting platform or other mounting devices where the antenna array is deployed e.g., a lamppost, etc.
Auto-calibration techniques are not practical due to the large amount of imperfections and typically lead to ill-conditioned problems.
Dedicated measurement campaigns are expensive and time-consuming. For example, in ultra-dense wireless communication systems there are in the order of 300 antenna arrays (each of which is mounted on a different lamppost) per square kilometres. In order to calibrate a single antenna array, many dedicated measurements taken in different locations need to be done. The number of measurements needed per antenna array depends on the desired density of the angular grid. For an angular grid of 1 degree, then 360×180 measurements are required. A high density of the angular grid leads to a more accurate location estimates.
In UL data transmissions, the data symbols are not typically known by the network. In antenna array calibration the UL signal needs to be known by the network in order to avoid gain and phase ambiguities. Moreover, most precoders and beamformers used in MIMO wireless communications exploit the multipath components of the channel for multiplexing or diversity gains. However, this is not desirable in antenna array calibration. In fact, in antenna array calibration the power of the multipath components should be minimized. Ideally, the UNd allocates power only to the LoS component between the UNd and the antenna array.